A globe sits on a geography teacher's desk. The diameter of the globe is 0.001 km. The earth has a diameter of 12, 713.54 km. Find the ratio of the volume of the globe to the volume of the earth.
To find the ratio of the volume of the globe to the volume of the earth, we need to calculate both volumes and then divide them.
The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where V represents the volume and r represents the radius.
Let's start by finding the volume of the globe on the teacher's desk, given that its diameter is 0.001 km.
1. Convert the diameter of the globe to radius by dividing it by 2:
Radius of the globe = diameter / 2
= 0.001 km / 2
= 0.0005 km
2. Now that we have the radius, we can calculate the volume of the globe:
V_globe = (4/3)πr^3
= (4/3)π(0.0005 km)^3
≈ 5.236 x 10^(-16) km^3
Now, let's find the volume of the entire Earth, knowing its diameter is 12,713.54 km:
3. Convert the diameter of the Earth to radius:
Radius of the Earth = 12,713.54 km / 2
= 6,356.77 km
4. Calculate the volume of the Earth:
V_earth = (4/3)πr^3
= (4/3)π(6,356.77 km)^3
≈ 1.083 x 10^12 km^3
Finally, we can find the ratio of the volume of the globe to the volume of the Earth:
Ratio = V_globe / V_earth
= (5.236 x 10^(-16) km^3) / (1.083 x 10^12 km^3)
≈ 4.84 x 10^(-28)
So, the ratio of the volume of the globe to the volume of the Earth is approximately 4.84 x 10^(-28).